A guide for the use of the function specification method for 2D inverse heat conduction problems

Abstract

The solution of the multidimensional inverse heat conduction problem (IHCP) requires much practice and several runs to determine the many parameters involved in the solution. This paper describes a step by step guide to identifying all of the parameters involved in the function specification method with spatial regularization: namely the number of future temperatures, the value of the regularization coefficient and the sensor locations. It also intends to show the new difficulties that arise from solving a 2D IHCP compared to a ID IHCP. The issue of finding the appropriate number of sensors and their locations so as to obtain a desired surface heat flux spatial resolution is addressed. An experimental set-up was built for the validation of the methodology. It also shows that the determination of surface temperature and flux that vary in both time and space from remote temperature measurements is possible when the sensors are properly placed.